Published on February 17, 2002; later updates.
I come back to the idea presented in a previous article: Dynamic versus Static in Lotto, Lottery Analysis. I ran my lottery software Combinations.exe to generate ranges of combinations around the field's midpoint or around the probability median for a 6/69 lotto game.
I applied the test to PA 6/69 lotto game (a very tough game, indeed; the jackpot odds are 1 in 119,877,472). I generated first 1000 combinations around the mid-point index: 59,938,736. That is, the lotto program generated combinations between the counts of 59,938,236 and 59,939,236.
Next, I checked for winners in the output file against real draws in PA 6/69 lotto (350 real lottery draws at my discretion). The mid-point output achieved 3 5 of 6 hits and 140 4 of 6 hits. The game odds are 1 in 317,000 for 5 of 6 and 1 in 4092 for 4 of 6. The 5 of 6 wins were recorded in 350 x 1000 = 350,000 combinations. Therefore, the mid-point strategy was about 3 times better than random play in the 5 of 6 situation. For the 4 of 6 case, 1 in 4092 applied to 350,000 lotto combinations translates into 85. The mid-point strategy hit 140 times, or about one and a half times better.
The next test was applied against the FFG median, instead of the mid-point. The FFG median is calculated in FFG for a degree of certainty DC equal to 50%. The FFG median is 83,092,731 for a 6/69 lotto game. A number of 1000 combinations were generated in the 83,092,231 – 83,093,231 range. The results were undoubtedly better. The strategy yielded 6 5 of 6 hits and 238 4 of 6 hits. Compared to purely random play, the FFG median strategy was 6 times better for 5 of 6 and about 3 times better in the 4 of 6 case.
I saw in the newsgroups similar tests applied to UK 6/49 lotto game, with lower odds than PA's 6/69 monster lotto. This time, the results were inverted: the mid-point strategy was favored! It became clear to me that this type of lottery strategy favors the probability (FFG) median in high odds games. The higher the odds, the better the FFG median strategy fares.
I did the test for 10000 lotto combinations against the same 350-draw data file (PA 6/69 lotto). I ran the test for both the midpoint and FFG median: 5000 below and 5000 above (actually, there are 10,001 lotto combinations, including the pivots). The results were dramatic!
1) The midpoint strategy performed worse than in the 1000 test; even worse than random play! It recorded 6 5 of 6 hits and 442 4 of 6 wins. That's about half of what lotto random play yields!
2) The 'probability median' strategy was far better than the '1000-combination test' and far-far better than random play.
- 1 6 of 6 (jackpot) win (34 times better than random play!);
- 75 5 of 6 hits;
- 2,232 4 of 6 wins!
Again, a random play for an equivalent amount of combinations (350 x 10001 = 3,500,350) should yield:
- 0.029 6 of 6 hits;
- 11 5 of 6 hits;
- 855 4 of 6 wins.
I compared these results with the results in a 6/49 game (UK, 642 draws).
The 10,001 runs did not yield jackpot wins. The lotto jackpot hits occurred at 50,001-combination runs!
1) Midpoint strategy:
- 27,439 hits (1 6 of 6 jackpot hit)
2) FFG median strategy:
- 34,616 hits (2 6 of 6 wins).
Now, the FFG median strategy was favored over the midpoint strategy!
It is very clear that this type of play favors the high odds games lotto by far. The lottery strategy is insignificant for lower odds games, such as pick-3 or pick-4 lotteries. I don't have a formula for it. I don't think this type of strategy has an under-pinning formula. The explanation relies on the type of combinations in various areas of the lotto field. The combinations in the FFG median area are largely part of the bell distribution. On the other hand, the purely random field includes many hardly-to-come-out-in-a-lifetime combinations. Combinations like 1-2-3-4-5-6 and the like, or 44-45-46-47-48-49 and the like.
Yes, some dudes will jump off: "They have an equal probability to come out!" But they won't come out. One can bet the entire budget surplus of the U.S. treasury in 2000 on lotto combinations such as the above. The results would be the red figures of the year 2002. I can give here a summary explanation, other than the Markov Chains. The lotto balls would need to be mixed for millions of hours before any drawing. Then, weird combinations would have a reasonable chance to come out. It is all about number of trials N.
Probability is viewed by many as a static phenomenon. "The individual probability in the pick-3 lottery is 1/1000. Therefore every lottery combination has an equal chance of appearance." That's correct, insofar as no dynamic processes are involved. But the lottery is a dynamic process. There is more to the picture than meets the eye. The formula of individual probability becomes just a part of inclusive systems (formulae). I have found that many random processes are ruled by the Fundamental Formula of Gambling (FFG). Equal individual probabilities do not lead to equal frequencies. The pick-3 combinations do not appear equally. There are 1000 possibilities in the pick-3 game. In 1000 tries, each and every combination should come out, right? NOT! FFG shows that only around 63 percent of the pick-3 combinations come out in 1000 draws, any 1000 consecutive draws. Some 37% of the pick-3 combination need more than 1000 draws to come out: 1500 draws, 3000 draws, even 6000 lottery drawings!
The chance to get EXACTLY 1 heads AND 1 tails in 2 tosses is 1 in 4. The event will be heads-tails or tails-heads. It means that if we toss the coin 2 times, and do such a thing 4 times, we can expect to get a result such as heads-tails or tails-heads. Sometimes, we may get it in the first try of 2 tosses; other times, we may have to wait 10 or more 2-toss tries.
Lotto 6 / 49 Report: SKIPS (ANY Position & Vertical POS) File: D6; Date: 08-11-2016 Line Any Any Any Any Any Any POT Pos Pos Pos Pos Pos Pos COL no 1 2 3 4 5 6 1 2 3 4 5 6 45 0- 3- 2- 2- 0- 2 3- 0- 45+ 57- 12+ 83+ 84+ 84+ 315 0- 0- 1- 1- 0- 3- 3- 20+ 5- 40+ 5- 0- 64- 64- 508 2- 0- 0- 4- 3+ 0 4- 2- 7- 27- 4- 7- 0 27- 885 1- 4- 0- 1- 0- 1- 4- 1- 4- 13- 30+ 9- 45+ 45+ 762 3- 5+ 0- 0- 3 1- 5- 22+ 25+ 0- 41+ 3- 1- 41- 626 0- 5- 0- 0- 2+ 1- 5- 47+ 33+ 110+ 29+ 6- 30- 110+ 295 5- 1- 2 1+ 0- 3- 5- 36+ 51- 11- 1- 29+ 11- 51- 978 1- 0- 1 5+ 4- 0- 5- 36+ 26+ 111+ 9- 25+ 0- 111+ 334 5 2- 5+ 1+ 1- 5- 5- 5- 39+ 37+ 1- 16- 5- 39+ 228 0 5+ 2- 4+ 1- 0- 5- 0 9+ 11- 25+ 8- 0- 25- 405 5- 0- 3+ 1- 4- 3 5- 5- 16+ 3 50+ 24- 50+ 50- 403 5+ 4+ 2- 0- 0- 5- 5- 5+ 48+ 73+ 23- 58+ 5- 73+ 429 0- 3- 0- 3+ 5+ 2- 5- 20+ 3- 0- 25- 40- 2- 40- 720 5- 0- 3- 0- 0- 2- 5- 14+ 0- 3- 0- 0- 21+ 21- 119 3- 2- 0 6+ 0- 4+ 6- 368+ 47+ 65+ 106+ 48+ 4+ 368+ ... 752 10+ 17+ 3- 17+ 9+ 58+ 58+ 10- 29- 9- 84+ 89+ 58+ 89- 676 2- 58+ 20+ 32+ 8+ 7 58+ 2- 67- 22- 32- 8+ 7 67- 482 4+ 15+ 49+ 16+ 20+ 60+ 60+ 7+ 15+ 63+ 16+ 26- 60+ 63+ 981 5+ 11+ 10+ 2- 10- 67+ 67+ 5+ 25- 10- 12- 10- 582+ 582+ 584 1- 1- 2- 3- 73+ 0- 73+ 1- 1- 33- 38- 113+ 0- 113- 165 6- 9- 4+ 7+ 76+ 0- 76+ 6- 9- 55+ 55+ 93+ 0- 93+
As for the midpoint and FFG median strategies presented in the beginning: I do not endorse them. I have no formula to lay a foundation. They may be expensive as well. They certainly need further lotto filtering, using LotWon filters. You should never — ever — apply ordinary cigarette-butt filters to smoking down the lottery odds!
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